Magnification and scale.

Step 1 of 6

Two lenses

Cells are too small for the eye to see: the eye picks out details of about a tenth of a millimetre, and a cheek cell is half that across. The Scene shows two microscopes looking at the same specimen, a scraping from inside a cheek: a light microscope on the left and an electron microscope on the right. Beside them are the two pictures each one sees.

Look inside has cut the microscopes open, so you can see the light’s path. The light microscope has two lenses one after the other: the objective, near the specimen, makes an enlarged picture, and the eyepiece, near the eye, enlarges that picture again. The turret carries four objectives: 4, 10, 40 and 100 times.

Step 2 of 6

Real size

Magnification says how many times bigger the picture is than the real thing:

$\text{magnification} = \frac{\text{image size}}{\text{real size}}$$\text{magnification} =$$\frac{\text{image size}}{\text{real size}}$⁠

So, knowing the magnification, you work out the real size by dividing: $\text{real size} = \dfrac{\text{image size}}{\text{magnification}}$$\text{real size} =$$\dfrac{\text{image size}}{\text{magnification}}$⁠. Cell sizes are measured in micrometres: 1 mm = 1000 µm.

Each of the two pictures beside the Scene is printed 20 mm wide.

Step 3 of 6

Choosing a magnification

Magnification in the Scene is written in powers of ten, as in the Unit on ratio and scale: 2 is $10^2$⁠, that is 100 times, and 3 is 1,000 times. The higher the magnification, the smaller the patch of specimen that fits in the picture.

Step 4 of 6

From a photograph

The same sum works for any photograph taken down a microscope, as long as you know the magnification. Books often add a scale bar to the photograph instead of giving the magnification.

Step 5 of 6

The smallest detail

You can magnify more and more, but what sets what you see is the resolution: the smallest distance at which two points still look like two and not one blur. Light is a wave, and a wave cannot pick out details much smaller than its wavelength. For a light microscope,

$d = \frac{0.61\,\lambda}{\mathrm{NA}}$$d =$$\frac{0.61\,\lambda}{\mathrm{NA}}$⁠

where $\lambda$⁠ is the wavelength and $\mathrm{NA}$⁠, the numerical aperture, measures how wide a cone of light the lens gathers. The caption under the light picture gives the objective in use and its $\mathrm{NA}$⁠.

Step 6 of 6

Empty magnification

The picture on the right, from the electron microscope, is much sharper. Electrons accelerated through a high voltage have a wavelength of a few picometres, a hundred thousand times shorter than light’s, so they separate details of less than a nanometre.